An apparatus of that kind is known from EP 1 593 533 A2. The known apparatus includes a hooked tool which is mounted movably to a tool holder by way of parallel links in two pivotal connection locations. The one end of the tool is in the form of a hooked engagement end and engages the tyre bead when removing the pneumatic tyre from the rim. Disposed at the other end of the tool is a pivotal connection location which is hingedly connected to the tool holder by way of one of the two link levers. At its one end the link lever is connected to the pivotal connection location and at its other end it is non-rotatably connected to a gear which belongs to a gear transmission mounted on the tool holder. The gear transmission has a further gear which is mounted rotatably to the tool holder and which can be caused to rotate by means of a control portion, to control the tool movement. A second pivotal connection location disposed between the two ends of the tool is supported on the tool holder by way of a second link lever. A relatively large number of hingedly interconnected components are required for controlling the movement of the tool when fitting and removing the pneumatic tyre.